经纬度坐标下的球面多边形面积计算公式

// calculate Area
        public static double calcArea(ArrayList PointX, ArrayList PointY, string MapUnits)
        {

            int Count = PointX.Count;
            if (Count > 2)
            {
                double mtotalArea = 0;

                if (MapUnits == "DEGREES")//经纬度坐标下的球面多边形
                {
                    double LowX = 0.0;
                    double LowY = 0.0;
                    double MiddleX = 0.0;
                    double MiddleY = 0.0;
                    double HighX = 0.0;
                    double HighY = 0.0;

                    double AM = 0.0;
                    double BM = 0.0;
                    double CM = 0.0;

                    double AL = 0.0;
                    double BL = 0.0;
                    double CL = 0.0;

                    double AH = 0.0;
                    double BH = 0.0;
                    double CH = 0.0;

                    double CoefficientL = 0.0;
                    double CoefficientH = 0.0;

                    double ALtangent = 0.0;
                    double BLtangent = 0.0;
                    double CLtangent = 0.0;

                    double AHtangent = 0.0;
                    double BHtangent = 0.0;
                    double CHtangent = 0.0;

                    double ANormalLine = 0.0;
                    double BNormalLine = 0.0;
                    double CNormalLine = 0.0;

                    double OrientationValue = 0.0;

                    double AngleCos = 0.0;

                    double Sum1 = 0.0;
                    double Sum2 = 0.0;
                    double Count2 = 0;
                    double Count1 = 0;

                    double Sum = 0.0;
                    double Radius = 6378000;

                    for (int i = 0; i < Count; i++)
                    {
                        if (i == 0)
                        {
                            LowX =(double) PointX[Count - 1] * Math.PI / 180;
                            LowY = (double)PointY[Count - 1] * Math.PI / 180;
                            MiddleX = (double)PointX[0] * Math.PI / 180;
                            MiddleY = (double)PointY[0] * Math.PI / 180;
                            HighX = (double)PointX[1] * Math.PI / 180;
                            HighY = (double)PointY[1] * Math.PI / 180;
                        }
                        else if (i == Count - 1)
                        {
                            LowX = (double)PointX[Count - 2] * Math.PI / 180;
                            LowY = (double)PointY[Count - 2] * Math.PI / 180;
                            MiddleX = (double)PointX[Count - 1] * Math.PI / 180;
                            MiddleY = (double)PointY[Count - 1] * Math.PI / 180;
                            HighX = (double)PointX[0] * Math.PI / 180;
                            HighY = (double)PointY[0] * Math.PI / 180;
                        }
                        else
                        {
                            LowX = (double)PointX[i - 1] * Math.PI / 180;
                            LowY = (double)PointY[i - 1] * Math.PI / 180;
                            MiddleX = (double)PointX[i] * Math.PI / 180;
                            MiddleY = (double)PointY[i] * Math.PI / 180;
                            HighX = (double)PointX[i + 1] * Math.PI / 180;
                            HighY = (double)PointY[i + 1] * Math.PI / 180;
                        }

                        AM = Math.Cos(MiddleY) * Math.Cos(MiddleX);
                        BM = Math.Cos(MiddleY) * Math.Sin(MiddleX);
                        CM = Math.Sin(MiddleY);
                        AL = Math.Cos(LowY) * Math.Cos(LowX);
                        BL = Math.Cos(LowY) * Math.Sin(LowX);
                        CL = Math.Sin(LowY);
                        AH = Math.Cos(HighY) * Math.Cos(HighX);
                        BH = Math.Cos(HighY) * Math.Sin(HighX);
                        CH = Math.Sin(HighY);

                        CoefficientL = (AM * AM + BM * BM + CM * CM) / (AM * AL + BM * BL + CM * CL);
                        CoefficientH = (AM * AM + BM * BM + CM * CM) / (AM * AH + BM * BH + CM * CH);

                        ALtangent = CoefficientL * AL - AM;
                        BLtangent = CoefficientL * BL - BM;
                        CLtangent = CoefficientL * CL - CM;
                        AHtangent = CoefficientH * AH - AM;
                        BHtangent = CoefficientH * BH - BM;
                        CHtangent = CoefficientH * CH - CM;

                        AngleCos = (AHtangent * ALtangent + BHtangent * BLtangent + CHtangent * CLtangent) / (Math.Sqrt(AHtangent * AHtangent + BHtangent * BHtangent + CHtangent * CHtangent) * Math.Sqrt(ALtangent * ALtangent + BLtangent * BLtangent + CLtangent * CLtangent));

                        AngleCos = Math.Acos(AngleCos);

                        ANormalLine = BHtangent * CLtangent - CHtangent * BLtangent;
                        BNormalLine = 0 - (AHtangent * CLtangent - CHtangent * ALtangent);
                        CNormalLine = AHtangent * BLtangent - BHtangent * ALtangent;

                        if (AM != 0)
                            OrientationValue = ANormalLine / AM;
                        else if (BM != 0)
                            OrientationValue = BNormalLine / BM;
                        else
                            OrientationValue = CNormalLine / CM;

                        if (OrientationValue > 0)
                        {
                            Sum1 += AngleCos;
                            Count1++;

                        }
                        else
                        {
                            Sum2 += AngleCos;
                            Count2++;
                            //Sum +=2*Math.PI-AngleCos;
                        }

                    }

                    if (Sum1 > Sum2)
                    {
                        Sum = Sum1 + (2 * Math.PI * Count2 - Sum2);
                    }
                    else
                    {
                        Sum = (2 * Math.PI * Count1 - Sum1) + Sum2;
                    }

                    //平方米
                    mtotalArea = (Sum - (Count - 2) * Math.PI) * Radius * Radius;
                }
                else
                { //非经纬度坐标下的平面多边形

                    int i, j;
                    //double j;
                    double p1x, p1y;
                    double p2x, p2y;
                    for ( i = Count - 1, j = 0; j < Count; i = j, j++)
                    {

                        p1x = (double)PointX[i];
                        p1y = (double)PointY[i];

                        p2x = (double)PointX[j];
                        p2y = (double)PointY[j];

                        mtotalArea += p1x * p2y - p2x * p1y;
                    }
                    mtotalArea /= 2.0;
                }
                return mtotalArea;
            }
            return 0;
        }